An isogeometric approach to cohesive zone modeling

Verhoosel, Clemens V.; Scott, Michael A.; Borst, René de; Hughes, Thomas J.R.

doi:10.1002/nme.3061

Cited by 174 publications

(135 citation statements)

References 38 publications

(51 reference statements)

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“…The extended finite element method has, in principle, fully decoupled the crack propagation path from the underlying mesh lay-out, see (Belytschko and Black, 1999;Moës et al, 1999), who applied the method to brittle fracture, and Wells and Sluys (2001); Moës and Belytschko (2002); Remmers et al (2003), who used a cohesive fracture model. More recently, the fact that knot insertion lowers the order of continuity in isogeometric finite element analysis has provided a novel way to introduce cracks in solids and structures (Verhoosel et al, 2011;Hosseini et al, 2014).…”

Section: Introductionmentioning

confidence: 99%

A numerical assessment of phase-field models for brittle and cohesive fracture: Γ-Convergence and stress oscillations

May

Vignollet

Borst

2015

European Journal of Mechanics - A/Solids

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142

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Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/) eprints@whiterose.ac.uk https://eprints.whiterose.ac.uk/ Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Takedown M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT• A numerical demonstration that in phase-field models for brittle fracture the smeared crack length does not necessarily converge to the discrete crack length upon mesh refinement.• A demonstration that the numerical results of boundary value problems that use the phase-field model for brittle fracture are very sensitive to how the boundary conditions are applied.• A proof that the phase-field model for cohesive fracture does not satisfy a two-dimensional patch test, even when the interpolation orders of the displacement field, the phase field and the crack-opening field are balanced. *Highlights (for review)M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPTA numerical assessment of phase-field models for brittle and cohesive fracture: Γ-convergence and stress oscillations AbstractRecently, phase-field approaches have gained popularity as a versatile tool for simulating fracture in a smeared manner. In this paper we give a numerical assessment of two types of phase-field models. For the case of brittle fracture we focus on the question whether the functional that describes the smeared crack surface approaches the functional for the discrete crack in the limiting case that the internal length scale parameter vanishes. By a one-dimensional example we will show that Γ-convergence is not necessarily attained numerically. Next, we turn attention to cohesive fracture. The necessity to have the crack opening explicitly available as input for the cohesive traction-relative displacement relation requires the independent interpolation of this quantity. The resulting three-field problem can be solved accurately on structured meshes when using a balanced interpolation of the field variables: displacements, phase field, and crac...

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Section: Introductionmentioning

confidence: 99%

A numerical assessment of phase-field models for brittle and cohesive fracture: Γ-Convergence and stress oscillations

May

Vignollet

Borst

2015

European Journal of Mechanics - A/Solids

Self Cite

142

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“…This property is useful in modelling traction-free cracks and adhesive interfaces (strong discontinuity) and layered structures with C 0 continuity between the layers (weak discontinuity) [13]. Figure 8 shows the steps in order to make a discontinuity in the thickness direction of a shell structure.…”

Section: Modelling Weak and Strong Discontinuities In The Displacemenmentioning

confidence: 99%

“…In a further study we will develop a versatile method to localize strong discontintuities. This can potentially be achieved by adopting a localized definition of the basis functions -as is essentially done in T-splines -and has already been demonstrated in the context of cohesive-zone modelling [13].…”

Section: Modelling Weak and Strong Discontinuities In The Displacemenmentioning

confidence: 99%

“…As a next step, in this contribution we adopt a higher-order interpolation in the thickness direction, which makes use of B-spline basis functions. An important advantage of using B-spline basis functions is their ability to model weak and strong discontinuity in the displacement field by knot insertion [13]. This is less straightforward using conventional finite elements.…”

Section: Introductionmentioning

confidence: 99%

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An isogeometric continuum shell element for non-linear analysis

Hosseini

Remmers

Verhoosel

et al. 2014

Computer Methods in Applied Mechanics and Engineering

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“…Thomas et al [59] developed a generalization of such technique. In recent years, the application of the T-spline in the IGA framework to different areas has been developed [60][61][62][63][64]. In the context of IGA-BEM Scott et al [58] extended the analysissuitable T-spline to unstructured meshes for elastostatic problems and developed a collocation procedure based on a generalization of the Grenville abscissae.…”

Section: Introductionmentioning

confidence: 99%

A 3d Isogeometrical Boundary Element Analysis for Non-Linear Gravity Wave Propagation

Maestre¹,

Pallarès²,

Cuesta³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. In this paper we describe a three-dimensional Isogeometric BEM in the time domain based on the T-spline and Non Uniform Rational B-Splines (NURBS) basis to study the free surface behavior. Traditionally, the Lagrange polynomials have been used to discretize the geometry and the BEMs variables. The Lagrange basis are discontinues across the elements although the physical variables are continuous. In dynamics problems with high mesh distortions this approach can produce numerical instabilities that can be quickly propagated. This problem could be overcome using T-spline or NURB basis. The main advantages of this approach are: (1) the control of the continuity and smoothness of the T-spline and NURBS basis, which makes the model numerically stable without the need of artificial smooth techniques;(2) the high order geometrical approximation by non-rational splines;(3) the refinement capabilities without affecting the geometry and BEM's variables; and (4) the direct integration with computer aid geometrical design tools. We use the concept of the Bézier extraction operation which provides an element point of view of the T-Spline and NURBS similar to the traditional finite element. The boundary integral Equation is solved at each time step by the GMRES algorithm and the time marching scheme is performed with a fourth-order Runge-Kutta method to update the model. Additionally, the hydrodynamic force is calculated by an auxiliary boundary equation. Some numerical benchmark examples are analysed to show the accuracy and the stability of the method 7967 J. Maestre, J. Pallarés and I. Cuesta

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An isogeometric approach to cohesive zone modeling

Cited by 174 publications

References 38 publications

A numerical assessment of phase-field models for brittle and cohesive fracture: Γ-Convergence and stress oscillations

A numerical assessment of phase-field models for brittle and cohesive fracture: Γ-Convergence and stress oscillations

An isogeometric continuum shell element for non-linear analysis

A 3d Isogeometrical Boundary Element Analysis for Non-Linear Gravity Wave Propagation

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